74.10.35 problem 37 (a)

Internal problem ID [16169]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.2, page 147
Problem number : 37 (a)
Date solved : Monday, March 31, 2025 at 02:45:50 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} 3 t^{2} y^{\prime \prime }-2 t y^{\prime }+2 y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 13

ode:=3*t^2*diff(diff(y(t),t),t)-2*t*diff(y(t),t)+2*y(t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ y = c_1 t +c_2 \,t^{{2}/{3}} \]

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 18

ode=3*t^2*D[y[t],{t,2}]-2*t*D[y[t],t]+2*y[t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to c_1 t^{2/3}+c_2 t \]

✓ Sympy. Time used: 0.154 (sec). Leaf size: 12

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(3*t**2*Derivative(y(t), (t, 2)) - 2*t*Derivative(y(t), t) + 2*y(t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{1} t^{\frac {2}{3}} + C_{2} t \]